a comparison of sassi2010 and sap2000 fixed-base

Transactions, SMiRT-22

San Francisco, California, USA - August 18-23, 2013 Division IX (include assigned division number from I to X)

A COMPARISON OF SASSI2010 and SAP2000 FIXED-BASE ANALYSIS RESULTS FOR VALIDATION OF A LARGE SCALE NUCLEAR

REACTOR BUILDING MODEL

Mohsin R. Khan1, Ming S. Yang1, J.C. Chen1, and Josh Parker2, Susan Farnworth2

1 ARES Corporation, 1990 N. California Blvd., Suite 500, Walnut Creek, CA 94526 ([email protected]) 2 NuScale Power, LLC, 1100 NE Circle Blvd., Suite 350, Corvallis, OR 97330 ABSTRACT

The enhanced version of the SASSI2010 computer program was used to analyze the soil-structure interaction (SSI) effect of the seismic design of a Nuclear Power Plant Reactor Building. To further validate the SASSI modeling capability, the results of SASSI fixed-base analyses for the large scale 3-D finite element model of the Reactor Building (RXB) were compared with those of SAP2000 fixed-base analysis. This paper summarizes the comparisons of bases shear forces, fundamental frequencies, transfer functions and in structure response spectra (ISRS) of the fixed-base RXB calculated by both computer programs.

In the fixed-base analysis, the RXB was assumed to be surface founded and subjected to the static gravity load and dynamic seismic excitation. The static 1g gravity load was applied in the three global directions to calculate the base shears. The seismic acceleration time histories compatible with the Certified Seismic Design Response Spectra (CSDRS) were applied to the RXB to calculate the structural response for ISRS generation.

The total base shear forces calculated by SASSI2010 agree well with those calculated by SAP2000. Comparisons of 5% response spectra at key locations in the RXB showed that comparable results were calculated by both computer programs for the large, complex RXB structure. In spite of significant differences in methodology between SASSI2010 and SAP2000, this study demonstrates that the base shear forces and response spectra calculated by both computer programs for the fixed-base analysis are comparable.

INTRODUCTION

For the seismic design, it is necessary to specify the design earthquake ground motion that is exerted on the plant structures of the soil-structure systems. The design ground motion was developed based on selected generic seismicity and geologic conditions of the site. The design ground motion was developed as free field ground response spectra to be the Safe Shutdown Earthquake (SSE). Based on modified Newmark-Hall Spectra and eight sets of design response spectra from eight licensees’ DCD applications, ARES has developed the CSDRS to be the SSE level for the conservative seismic design of the RXB, (Khan et al, 2011). In addition, the CSDRS was modified to incorporate the high frequency contents observed in many Eastern United States (EUS) sites and to envelope the probabilistic seismic hazard assessment (PSHA) spectra for 3 EUS rock sites. The enveloping spectra are termed as Generic High Frequency Hard Rock Response Spectra (GHFHRRS). Acceleration time histories were generated so that their response spectra closely match the target design spectra per requirements specified in Section 2.4 of ASCE/SEI 43-05 and NUREG-0800 SRP 3.7.1. Five sets of time histories were generated to match the CSDRS and two sets match the GHFHRRS. Six sets were obtained by modifying selected

22nd Conference on Structural Mechanics in Reactor Technology


earthquake records and two sets by synthetic harmonics. Figure 1 shows the 5% damped N-S response spectra of six CSDRS compatible time histories. Figure 2 shows the N-S component of the CSDRS compatible acceleration time history used for the fixed-base analyses.

Figure1. N-S 5% Damped Design Spectra.

Figure 2. CSDRS Acceleration Time History.

To cover a wide range of site soil conditions in the design, a set of generic soil profile consisting of several site conditions have been developed for the analysis of the Nuclear RXB. Site response analyses were performed for each site to obtain strain

compatible soil properties for all CSDRS or GHFHRRS compatible ground motions. The average properties for CSDRS or GHFHRRS motions were used for the SSI analyses.

The SASSI2010 computer program was used to analyze the soil-structure interaction responses of the Nuclear RXB. The verification and validation (V&V) effort for the new SASSI codes was documented in ARES calculation report (Ming et al., 2012). To further enhance the V&V effort for the SASSI2010, it was determined to perform the fixed-base analysis of the RXB using SASSI20102 and compare the results with those calculated by the SAP2000. This paper presents comparisons of base shear forces, fundamental frequencies, displacement time histories, and ISRS at selected key locations. The SAP2000 structural analysis results for the RXB up to 30% design completion have been documented in the ARES report.

Two cases of analyses were performed: (1) treating the RXB as a fixed-base surface founded structure and, (2) treating the RXB as an embedded structure with the base founded at approximately 100 feet below the ground surface. The static 1 g load was applied to the fixed-base structure in three global directions to calculate the base shears. The CSDRS compatible time histories were used as input to calculate RXB responses for ISRS generation.

REACTOR BUILDING

Only the results of the RXB analysis are described in this paper. The RXB is a generally rectangular design. It is embedded about 100ʹ below ground and rises about 100ʹ above ground. The major structural elements, equipment, and components consist of basement, pools, roof structure, RXB outer walls, RXB pool walls, RXB slabs, concrete pilasters and beams, equipment hatches in floors, reactor building crane, roof support pilasters and other miscellaneous structures.



SAP2000 RXB MODEL AND ANALYSIS

The fixed-based SAP2000 finite element model of the RXB was used to generate the ISRS for preliminary design evaluation of equipment. The X-, Y-, and Z-axes are in the E-W, N-S, and vertical directions, respectively.

The roof, floor slabs, and walls of the RXB were modeled at their neutral planes using thick-shell elements. The beams, columns, and pilasters were modeled at their neutral axes using beam elements. Equipment, RPV modules, and equipment supports were modeled with beam elements. Rigid spring elements were used at the base to simulate the fixed base and to facilitate base shear calculations. The structural model includes structural and non-structural masses.

Loads and load combinations include dead and live loads, soil pressure (static and dynamic), hydrostatic pressure, snow load, wind and tornado loads. Water weights are considered as added weight to all pool wall nodes. Equipment weights are added at appropriate nodes. To account for live load inertial effects, 25% percent of the live load has been added to slab masses.

Two analysis models were created to consider the conditions of cracked and uncracked concrete behavior. However, only uncracked results are presented herein. Uncracked case uses full bending properties for concrete walls and slabs, whereas, the cracked case uses half of the bending properties for the concrete walls and slabs and higher damping. The geometry and applied loads for two models are identical except the assigned concrete properties and damping. For the cracked model, the out-of-plane stiffness is considered cracked for roof, walls, and all floor slabs other than the base. The sectional properties of the out-of-plane stiffness of the cracked elements are reduced to half. The in-plane stiffnesses remain unchanged. The fixed-base model has restrained nodes at the foundation. The RXB was supported on over 2000 zero-length rigid spring elements at the bottom of the foundation. The analysis and design methods used in the development of the SAP2000 analysis model are consistent with the ASCE Standard 4 and the ASCE/SEI 43-05.

The mode superposition approach with constant 4% modal damping was used in the analysis for the uncracked condition and the Ritz method was used to calculate modal frequencies and mode shapes.

SASSI2010 ANALYSIS

SASSI2010 (Ostadan et al. 2012) has been developed for analyzing the effect of SSI on the

dynamic response of structures using the substructure method. The methodology is completely different from SAP2000. The method is formulated from the solution procedures in the frequency domain using complex response method and the finite element technique. This method has the advantage of avoiding the scattering problem and employing a special technique (Tarjirian, 1981) to calculate frequency dependent 3-D impedance matrix. The method is capable of analyzing SSI effect of arbitrary shapes of surface founded and embedded structures subjected to seismic motions.



Figure 3. 3D Cross Sectional View of SSI Analysis Case.

The modified subtraction method (MSM) was used for the preliminary SSI analysis of the RXB for study and design optimization.

The SASSI analysis was performed according to the applicable codes such as ASCE 4-98 and ASCE/SEI 43-05. The entire SAP2000 structural model including all nodes, elements, and lumped masses was converted to a SASSI model for the SSI analysis. Only the uncracked model was used for SASSI analysis for comparison evaluation. A pictorial view of the SSI analysis problem is shown in Figure 3. The isometric view of converted SASSI model is shown in Figure 8. The interaction nodes of the excavated soil element were included as shown in the bottom part of Figure 8. Table 1 summarizes the approximate numbers of each element category and the interaction node for the surface founded model. To simulate the fixed-base condition in SASSI model, the RXB was placed on top of a rigid half-space with the S-wave velocity of 80,000 fps and P-wave velocity of 160,000 fps. As implemented in the SAP2000 analysis, the RXB structure was connected to the rigid half space using 3D rigid springs. To simulate a static gravity load condition, the structure was subjected to a slow-rise and slow-decay acceleration step function of 1g peak ground acceleration (PGA).

Table 1: Fixed-Base SASSI2010 Model Summary.

Fixed Base SASSI Model Summary Total Number Number of Solid Elements 400 Number of Beam Elements 1,700

Number of Thick Shell Elements 25,000 Total Number of Elements 30,000

Total Number of Nodes 55,000 Total Number of Lumped Masses 15,000

Total Number of Degrees of Freedom 153,000 BASE SHEAR COMPARISON BETWEEN SASSI2010 AND SAP2000

The comparison of base shears obtained from SASSI2010 and SAP2000 fixed-base analyses are presented. The SASSI model was subjected to a simulated gravity load of 1g step acceleration shown in Figure 4. Due to the long rising (20 seconds), decaying (20 seconds), and constant 1g amplitude (25 seconds) durations in the loading function, the dynamic effect was essentially eliminated and the loading is equivalent to the static one. The input was applied in X-, Y-, and Z-directions and designated by 1GX, 1GY, and 1GZ, respectively. The base shears are calculated by the summation of the forces in all rigid springs at the bottom of the foundation.



The base spring forces due to the static step inputs in X-,Y-,and Z-directions are shown in Figures 5, 6, and 7, respectively. The total shear force comparisons are shown in Table 2. The differences are less than 1%. These calculation results indicate the agreement is exceedingly well in calculating the base shear forces by the two programs. Other than the differences due to numerical truncation, this comparison confirms that the SAP2000 and SASSI model have identical weights.

Figure 4. 1g Step Function.

Figure 5. Base Spring Forces due to 1GX.

Figure 6. Base Spring Forces due to 1GY.

Figure 7. Base Spring Forces due to 1GZ.

Table: 2 Base Shear Ratio Comparison Calculated by 1g Step Function Input in SASSI and Lin Static SAP2000.

Output Ratio Case

1GX 1.007

1GY 1.008

1GZ 1.004

FIXED-BASE FREQUENCY COMPARISON

The fundamental model frequencies of the fixed-base RXB can be examined from the transfer functions calculated by SASSI2010. The frequencies at the peaks of the calculated transfer function should correspond to the predominant modes of the SAP2000 calculation at the node. The typical transfer function at Node 45204 was examined. This node is located at the top, east corner of an 8 foot thick wall. Figures 8 through 10 show the transfer functions in X-, Y-, and Z -directions due to the input of each of the X, Y, and Z components, respectively. The first modal frequencies at Node 45204 in X-, Y-, and Z-directions calculated by SASSI2010 and SAP2000 are compared in Table 3. That the frequency differences are small implies that the stiffnesses and masses of the SASP2000 RXB model were successfully duplicated by the SASSI2010 model.

22nd Conference on Structural Mechanics in Reactor Technology San Francisco, California, USA - August 18-23, 2013

Division IX (include assigned division number from I to X)

Figure 8. Fixed Base X Transfer Function at

N45204 due to X-Input.

Figure 9. Fixed Base Y Transfer Function at

N45204 due to Y-Input.

Figure 10. Fixed-Base Z transfer Function at

N45204 due to Z-Input.

Table 3: Difference in Fixed-Base RXB

Frequency (Hz) by SASSI2010 and SAP2000.

Program X-Mode Y-Mode Z Mode

Difference -1.3% +1.0% +1.9%

RESPONSE SPECTRA COMPARISONS

The typical significant responses calculated by SASS2010 and SAP2000 for the fixed-base RXB model subjected to three components of CSDRS control motions are compared. As shown in Figures 11 and 12, where the 5% damped Y-ISRS at Nodes 45204 and 51430 are presented, the ISRS compare well. Since the stiffness, masses, and damping properties of the structural elements and the boundary conditions are identically modeled by the two programs, it is expected that ISRS obtained from the two programs be in reasonable agreement even though the methodologies employed by the two programs are significantly different.

Figure 11. Y-ISRS Comparison at N45204.

Figure 12. Y-ISRS Comparison at N51430.



RELATIVE DISPLACEMENT TIME HISTORIES COMPARISONS

Table 4 show the relative displacements calculated by the two programs at Nodes 51430, which located at N-W corner at the roof-wall junction and at about 50ʹ above ground. The ground input and total response displacements at Node 51430 plus the relative displacement, which was obtained by subtracting the ground input displacement from the total response displacement, are shown in Figure 13. For comparison, the relative Y-displacement time histories by the two programs at Node 51430 are shown in Figure 14. SAP2000 calculated higher displacements than SASSI2010. This may be due to small damping mismatch as the two programs use different approaches to account for the structural damping.

Table 4: Ratio of Peak Relative Displacements by SASSI2010 and SAP2000.

Direction Ratio UX 1.24 UY .985 UZ 1.14

Figure 13. SASSI Input, Total, and Relative Displacements in Y-Direction at N51430.

Figure 14. Comparison of Y Relative Displacements at Node 51430.



SUMMARY AND CONCLUSIONS

The enhanced version of the SASSI2010 computer program is being used to analyze the soil-structure interaction effect on the seismic responses of the Nuclear RXB. To demonstrate the SASSI modeling capability for a large structure, the results of the SASSI2010 analysis for the large 3-D finite element model of the fixed-base RXB were compared to those of the fixed-base analysis of the RXB by SAP2000. This paper summarizes the comparisons of base shear forces, modal frequencies, and ISRS calculated by both computer programs.

The static 1g load was used in the analysis for the calculation of base shear while one of the CSDRS-compatible acceleration time histories was used in the analysis for the calculation of ISRS.

The total base shear forces calculated by SASSI2010 agree exceedingly well with those calculated by SAP2000. Comparisons of 5% response spectra at key significant response locations in the RXB showed compatible results given by both programs for such a large scale structure modeled by detailed finite element modeling. In spite of significant differences in methodology between SASSI2010 and SAP2000, this study has demonstrated that the base shear forces, modal frequencies, ISRS, and displacements calculated by both programs for the fixed-base analysis are remarkably comparable.

REFERENCES

ARES (2012). “SASSI2010 Verification and Validation Packages,” ARES Corporation. Computer and Structures, Inc., Berkeley. (2012). SAP2000 Advanced Version 15.1.0 Khan, M., et al (2011). “Certified Seismic Design Response Spectra and Time History Generation for

Advanced Reactor License Submittal,” SMiRT 21. Khan, M., et al (2011). “Development of Generic Soil Profiles and Soil Data Development for SSI

Analysis,” SMiRT 21. Ostadan, F. and Deng, N. (2012). SASSI2010 Version 1.0, UM_SASSI2010_TOCver1-0.doc SAP2000 Advanced Version 15.1.0, Computer and Structures, Inc., Berkeley, California. Tarjirian, F. (1981). “Impedance Matrices and Interpolation Techniques for 3-D Interaction Analysis by

the Flexible Volume Method,” Ph. D. Dissertation, UCB, 1981

a comparison of sassi2010 and sap2000 fixed-base

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